file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.pow_monotone | [] | [
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101
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448,
1
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Mathlib/Algebra/Lie/Solvable.lean | LieAlgebra.solvable_iff_equiv_solvable | [
{
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255,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/UniformSpace/Basic.lean | UniformContinuousOn.continuousOn | [
{
"state_after": "α : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ?u.150229\ninst✝¹ : UniformSpace α\ninst✝ : UniformSpace β\nf : α → β\ns : Set α\nh : UniformContinuous (restrict s f)\n⊢ ContinuousOn f s",
"state_before": "α : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ?u.150229\... | [
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Mathlib/SetTheory/Cardinal/Cofinality.lean | Ordinal.ord_cof_le | [] | [
297,
55
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Mathlib/Logic/Equiv/Set.lean | Equiv.Set.image_symm_apply | [
{
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... | [
494,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.get?_mem | [
{
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"state_before": "α : Type u\nβ : Type v\nγ : Type w\ns : WSeq α\na : α\nn : ℕ\n⊢ some a ∈ get? s n → a ∈ s",
"tactic": "revert s"
},
{
"state_after": "case zero\nα : Type u\nβ : Type... | [
1002,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
989,
1
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Mathlib/MeasureTheory/Measure/GiryMonad.lean | MeasureTheory.Measure.join_dirac | [] | [
235,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/VectorBundle/Basic.lean | VectorPrebundle.totalSpaceMk_preimage_source | [] | [
955,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
953,
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Mathlib/Topology/Order/Basic.lean | LinearOrderedAddCommGroup.tendsto_nhds | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝² : TopologicalSpace α\ninst✝¹ : LinearOrderedAddCommGroup α\ninst✝ : OrderTopology α\nl : Filter β\nf g : β → α\nx : Filter β\na : α\n⊢ Tendsto f x (𝓝 a) ↔ ∀ (ε : α), ε > 0 → ∀ᶠ (b : β) in x, abs (f b - a) < ε",
"ta... | [
1869,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/CategoryTheory/Limits/Shapes/Diagonal.lean | CategoryTheory.Limits.pullbackDiagonalMapIdIso_hom_snd | [
{
"state_after": "C : Type u_2\ninst✝⁵ : Category C\nX Y Z : C\ninst✝⁴ : HasPullbacks C\nS T : C\nf : X ⟶ T\ng : Y ⟶ T\ni : T ⟶ S\ninst✝³ : HasPullback i i\ninst✝² : HasPullback f g\ninst✝¹ : HasPullback (f ≫ i) (g ≫ i)\ninst✝ :\n HasPullback (diagonal i) (map (f ≫ i) (g ≫ i) i i f g (𝟙 S) (_ : (f ≫ i) ≫ 𝟙 S... | [
253,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
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] |
Mathlib/Order/BooleanAlgebra.lean | sup_compl_eq_top | [] | [
563,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
562,
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Mathlib/Data/Finsupp/Defs.lean | Finsupp.mulHom_ext | [
{
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1158,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1149,
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Mathlib/Algebra/Order/LatticeGroup.lean | LatticeOrderedCommGroup.neg_eq_pos_inv | [] | [
260,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
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Mathlib/RingTheory/Polynomial/Basic.lean | Polynomial.coeff_toSubring' | [] | [
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25
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366,
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Mathlib/Deprecated/Subgroup.lean | IsSubgroup.mem_norm_comm_iff | [] | [
229,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/Combinatorics/SetFamily/Shadow.lean | Finset.mem_upShadow_iff_erase_mem | [
{
"state_after": "case refine'_1\nα : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\n𝒜 : Finset (Finset α)\ns t : Finset α\na : α\nk r : ℕ\n⊢ (∃ t, t ∈ 𝒜 ∧ ∃ a x, insert a t = s) → ∃ a, a ∈ s ∧ erase s a ∈ 𝒜\n\ncase refine'_2\nα : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\n𝒜 : Finset (Finset... | [
232,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/RingTheory/DedekindDomain/Ideal.lean | Ideal.prime_iff_isPrime | [] | [
723,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
722,
1
] |
Mathlib/Topology/LocallyFinite.lean | LocallyFinite.closure_iUnion | [
{
"state_after": "case h\nι : Type u_1\nι' : Type ?u.7433\nα : Type ?u.7436\nX : Type u_2\nY : Type ?u.7442\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nf g : ι → Set X\nh : LocallyFinite f\nx : X\n⊢ x ∈ closure (⋃ (i : ι), f i) ↔ x ∈ ⋃ (i : ι), closure (f i)",
"state_before": "ι : Type u_1\nι'... | [
134,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
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Mathlib/Algebra/Lie/IdealOperations.lean | LieSubmodule.mono_lie | [
{
"state_after": "R : Type u\nL : Type v\nM : Type w\nM₂ : Type w₁\ninst✝¹⁰ : CommRing R\ninst✝⁹ : LieRing L\ninst✝⁸ : LieAlgebra R L\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\ninst✝⁵ : LieRingModule L M\ninst✝⁴ : LieModule R L M\ninst✝³ : AddCommGroup M₂\ninst✝² : Module R M₂\ninst✝¹ : LieRingModule L M₂\n... | [
159,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
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src/lean/Init/SimpLemmas.lean | Bool.true_and | [
{
"state_after": "no goals",
"state_before": "b : Bool\n⊢ (true && b) = b",
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}
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113,
87
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
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Mathlib/Data/Sum/Interval.lean | Sum.Ioc_inl_inr | [] | [
169,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.tan_mul_cos | [
{
"state_after": "no goals",
"state_before": "x✝ y x : ℂ\nhx : cos x ≠ 0\n⊢ tan x * cos x = sin x",
"tactic": "rw [tan_eq_sin_div_cos, div_mul_cancel _ hx]"
}
] | [
981,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
980,
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Mathlib/Topology/MetricSpace/Basic.lean | Metric.bounded_ball | [] | [
2325,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2324,
1
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Mathlib/Data/Finsupp/Defs.lean | Finsupp.single_of_single_apply | [
{
"state_after": "α : Type u_1\nβ : Type ?u.44418\nγ : Type ?u.44421\nι : Type ?u.44424\nM : Type u_2\nM' : Type ?u.44430\nN : Type ?u.44433\nP : Type ?u.44436\nG : Type ?u.44439\nH : Type ?u.44442\nR : Type ?u.44445\nS : Type ?u.44448\ninst✝ : Zero M\na✝ a'✝ : α\nb✝ : M\na a' : α\nb : M\n⊢ single a (if a' = a ... | [
358,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
351,
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] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.isCycle_swap | [
{
"state_after": "no goals",
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"tactic": "rwa [swap_apply_right]"
},
{
"state_after": "ι : Type ?u.409761\nα : Type u_1\nβ : Type ?u.409767\nf g :... | [
373,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
367,
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] |
Mathlib/Analysis/Convex/Star.lean | StarConvex.smul | [] | [
293,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
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Mathlib/Algebra/DirectSum/Algebra.lean | DirectSum.algHom_ext' | [] | [
122,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
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] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.aemeasurable_withDensity_ennreal_iff | [
{
"state_after": "case mp\nα : Type u_1\nβ : Type ?u.1777927\nγ : Type ?u.1777930\nδ : Type ?u.1777933\nm : MeasurableSpace α\nμ ν : Measure α\nf : α → ℝ≥0\nhf : Measurable f\ng : α → ℝ≥0∞\n⊢ AEMeasurable g → AEMeasurable fun x => ↑(f x) * g x\n\ncase mpr\nα : Type u_1\nβ : Type ?u.1777927\nγ : Type ?u.1777930\... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1724,
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Mathlib/Data/Finset/Basic.lean | Finset.biUnion_singleton_eq_self | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.519986\nγ : Type ?u.519989\ninst✝¹ : DecidableEq β\ns s₁ s₂ : Finset α\nt t₁ t₂ : α → Finset β\ninst✝ : DecidableEq α\nx : α\n⊢ x ∈ Finset.biUnion s singleton ↔ x ∈ s",
"tactic": "simp only [mem_biUnion, mem_singleton, exists_prop, ... | [
3634,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3633,
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] |
Mathlib/Data/Polynomial/Derivative.lean | Polynomial.derivative_bit1 | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\nι : Type y\nA : Type z\na✝ b : R\nn : ℕ\ninst✝ : Semiring R\na : R[X]\n⊢ ↑derivative (bit1 a) = bit0 (↑derivative a)",
"tactic": "simp [bit1]"
}
] | [
152,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
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] |
Mathlib/Algebra/EuclideanDomain/Basic.lean | EuclideanDomain.zero_mod | [] | [
80,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
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] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.nat_succ | [] | [
1377,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1376,
1
] |
Mathlib/Data/Set/Finite.lean | Set.iUnion_iInter_of_monotone | [] | [
1526,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1523,
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src/lean/Init/SimpLemmas.lean | bne_self_eq_false' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\na : α\n⊢ (a != a) = false",
"tactic": "simp [bne]"
}
] | [
152,
95
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
152,
9
] |
Mathlib/Topology/Algebra/Order/IntermediateValue.lean | IsPreconnected.intermediate_value₂ | [] | [
101,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.sqrtTwoAddSeries_succ | [
{
"state_after": "no goals",
"state_before": "x✝ x : ℝ\nn : ℕ\n⊢ sqrtTwoAddSeries x (n + 1 + 1) = sqrtTwoAddSeries (sqrt (2 + x)) (n + 1)",
"tactic": "rw [sqrtTwoAddSeries, sqrtTwoAddSeries_succ _ _, sqrtTwoAddSeries]"
}
] | [
714,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
711,
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Mathlib/Data/Finset/Option.lean | Finset.mem_insertNone | [
{
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"tactic": "cases h"
},
{
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"state_before": "α : Type u_1\nβ : Type ?u.2246\ns : Finset α\na : α\n⊢ some a = none ∨ some a ∈ (map Embedding.some ... | [
75,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/SetTheory/Ordinal/NaturalOps.lean | Ordinal.nadd_assoc | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.mapLe_isTrail | [] | [
1609,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1607,
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Mathlib/Topology/Homotopy/HomotopyGroup.lean | GenLoop.Homotopic.diagonal | [
{
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"state_before": "X : Type u\ninst✝¹ : TopologicalSpace... | [
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44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Set/Finite.lean | Set.card_lt_card | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/MetricSpace/Completion.lean | UniformSpace.Completion.mem_uniformity_dist | [
{
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142,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/CategoryTheory/Bicategory/Basic.lean | CategoryTheory.Bicategory.whiskerRight_comp_symm | [
{
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"tactic": "simp"
}
] | [
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74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
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Mathlib/LinearAlgebra/Multilinear/Basic.lean | MultilinearMap.map_neg | [
{
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Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.PushoutCocone.condition_zero | [
{
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797,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
795,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.Nonempty.smul_set | [] | [
408,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
407,
1
] |
Mathlib/Analysis/NormedSpace/lpSpace.lean | algebraMap_memℓp_infty | [
{
"state_after": "α : Type ?u.798282\nE : α → Type ?u.798287\np q : ℝ≥0∞\ninst✝⁴ : (i : α) → NormedAddCommGroup (E i)\nI : Type u_1\n𝕜 : Type u_3\nB : I → Type u_2\ninst✝³ : NormedField 𝕜\ninst✝² : (i : I) → NormedRing (B i)\ninst✝¹ : (i : I) → NormedAlgebra 𝕜 (B i)\ninst✝ : ∀ (i : I), NormOneClass (B i)\nk ... | [
962,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
960,
1
] |
Mathlib/Order/UpperLower/Basic.lean | isLowerSet_sUnion | [] | [
126,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Order/Antisymmetrization.lean | antisymmRel_swap | [] | [
47,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
1
] |
Mathlib/FieldTheory/IntermediateField.lean | mem_subalgebraEquivIntermediateField_symm | [] | [
765,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
762,
1
] |
Mathlib/Topology/Order/Hom/Basic.lean | ContinuousOrderHom.comp_apply | [] | [
171,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | Real.hasStrictDerivAt_const_rpow | [
{
"state_after": "no goals",
"state_before": "x✝ y z a : ℝ\nha : 0 < a\nx : ℝ\n⊢ HasStrictDerivAt (fun x => a ^ x) (a ^ x * log a) x",
"tactic": "simpa using (hasStrictDerivAt_const _ _).rpow (hasStrictDerivAt_id x) ha"
}
] | [
329,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
1
] |
Mathlib/Analysis/Convex/Quasiconvex.lean | Antitone.quasiconcaveOn | [] | [
225,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Prod.lean | hasFDerivAt_prod_mk_left | [] | [
89,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Topology/Algebra/Order/ExtrClosure.lean | IsExtrOn.closure | [] | [
42,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
40,
11
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.inv_mem_inv | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.30467\nα : Type u_1\nβ : Type ?u.30473\nγ : Type ?u.30476\nδ : Type ?u.30479\nε : Type ?u.30482\ninst✝ : InvolutiveInv α\nf g : Filter α\ns : Set α\nhs : s ∈ f\n⊢ s⁻¹ ∈ f⁻¹",
"tactic": "rwa [mem_inv, inv_preimage, inv_inv]"
}
] | [
241,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/MeasureTheory/Group/FundamentalDomain.lean | MeasureTheory.IsFundamentalDomain.nullMeasurableSet_smul | [] | [
197,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/CategoryTheory/Sites/SheafOfTypes.lean | CategoryTheory.Equalizer.Presieve.compatible_iff | [
{
"state_after": "C : Type u₁\ninst✝¹ : Category C\nP : Cᵒᵖ ⥤ Type (max v₁ u₁)\nX : C\nR : Presieve X\nS : Sieve X\ninst✝ : HasPullbacks C\nx : FirstObj P R\n⊢ Presieve.FamilyOfElements.PullbackCompatible ((firstObjEqFamily P R).hom x) ↔ firstMap P R x = secondMap P R x",
"state_before": "C : Type u₁\ninst✝... | [
988,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
978,
1
] |
Mathlib/Topology/PathConnected.lean | PathConnectedSpace.exists_path_through_family | [
{
"state_after": "X : Type u_1\nY : Type ?u.695592\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y\nx y z : X\nι : Type ?u.695607\nF : Set X\ninst✝ : PathConnectedSpace X\nn : ℕ\np : Fin (n + 1) → X\nthis : IsPathConnected univ\n⊢ ∃ γ, ∀ (i : Fin (n + 1)), p i ∈ range ↑γ",
"state_before": "X : Typ... | [
1176,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1172,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_comp_val_Iic_atBot | [
{
"state_after": "ι : Type ?u.341777\nι' : Type ?u.341780\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.341789\ninst✝ : SemilatticeInf α\na : α\nf : α → β\nl : Filter β\n⊢ Tendsto (fun x => f ↑x) atBot l ↔ Tendsto (f ∘ Subtype.val) atBot l",
"state_before": "ι : Type ?u.341777\nι' : Type ?u.341780\nα : Type u_1\... | [
1636,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1634,
1
] |
Mathlib/Data/List/Basic.lean | List.bind_singleton | [] | [
500,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
499,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Base.lean | Real.logb_nonneg_iff_of_base_lt_one | [
{
"state_after": "no goals",
"state_before": "b x y : ℝ\nb_pos : 0 < b\nb_lt_one : b < 1\nhx : 0 < x\n⊢ 0 ≤ logb b x ↔ x ≤ 1",
"tactic": "rw [← not_lt, logb_neg_iff_of_base_lt_one b_pos b_lt_one hx, not_lt]"
}
] | [
306,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
1
] |
Mathlib/Algebra/Hom/Units.lean | Units.val_pow_eq_pow_val | [] | [
123,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.IsCycleOn.conj | [
{
"state_after": "ι : Type ?u.1643430\nα : Type u_1\nβ : Type ?u.1643436\nf g : Perm α\ns t : Set α\na b x✝ y✝ : α\nh : IsCycleOn f s\nx : α\nhx : x ∈ ↑g⁻¹ ⁻¹' s\ny : α\nhy : y ∈ ↑g⁻¹ ⁻¹' s\n⊢ SameCycle (g * f * g⁻¹) x y",
"state_before": "ι : Type ?u.1643430\nα : Type u_1\nβ : Type ?u.1643436\nf g : Perm α... | [
792,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
789,
1
] |
Mathlib/CategoryTheory/Over.lean | CategoryTheory.Over.map_obj_hom | [] | [
181,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.nonempty_range_iff | [] | [
3044,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3042,
1
] |
Mathlib/Algebra/RingQuot.lean | RingQuot.Rel.star | [
{
"state_after": "no goals",
"state_before": "R : Type u₁\ninst✝⁵ : Semiring R\nS : Type u₂\ninst✝⁴ : CommSemiring S\nA : Type u₃\ninst✝³ : Semiring A\ninst✝² : Algebra S A\nr : R → R → Prop\nT : Type u₄\ninst✝¹ : Semiring T\ninst✝ : StarRing R\nhr : ∀ (a b : R), r a b → r (Star.star a) (Star.star b)\na b :... | [
559,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
551,
1
] |
Mathlib/RingTheory/Polynomial/Dickson.lean | Polynomial.dickson_of_two_le | [
{
"state_after": "case intro\nR : Type u_1\nS : Type ?u.68228\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nk : ℕ\na : R\nn : ℕ\nh : 2 ≤ 2 + n\n⊢ dickson k a (2 + n) = X * dickson k a (2 + n - 1) - ↑C a * dickson k a (2 + n - 2)",
"state_before": "R : Type u_1\nS : Type ?u.68228\ninst✝¹ : CommRing R\ninst✝ : Co... | [
93,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | IsGLB.csInf_eq | [] | [
555,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
554,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.IsImage.compl | [] | [
551,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
551,
11
] |
Mathlib/Algebra/Order/Field/Basic.lean | add_sub_div_two_lt | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.185600\nα : Type u_1\nβ : Type ?u.185606\ninst✝ : LinearOrderedField α\na b c d : α\nn : ℤ\nh : a < b\n⊢ a + (b - a) / 2 < b",
"tactic": "rwa [← div_sub_div_same, sub_eq_add_neg, add_comm (b / 2), ← add_assoc, ← sub_eq_add_neg, ←\n lt_sub_iff_ad... | [
919,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
917,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiff.div_const | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\ninst✝¹⁶ : NontriviallyNormedField 𝕜\nD : Type uD\ninst✝¹⁵ : NormedAddCommGroup D\ninst✝¹⁴ : NormedSpace 𝕜 D\nE : Type uE\ninst✝¹³ : NormedAddCommGroup E\ninst✝¹² : NormedSpace 𝕜 E\nF : Type uF\ninst✝¹¹ : NormedAddCommGroup F\ninst✝¹⁰ : NormedSp... | [
1482,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1481,
1
] |
Mathlib/LinearAlgebra/Dual.lean | Submodule.dualCoannihilator_sup_eq | [] | [
908,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
906,
1
] |
Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.bijective_respectsIso | [] | [
672,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
670,
1
] |
Mathlib/GroupTheory/Congruence.lean | Con.conGen_le | [
{
"state_after": "M : Type u_1\nN : Type ?u.26925\nP : Type ?u.26928\ninst✝² : Mul M\ninst✝¹ : Mul N\ninst✝ : Mul P\nc✝ : Con M\nr : M → M → Prop\nc : Con M\nh : ∀ (x y : M), r x y → Setoid.r x y\n⊢ sInf {s | ∀ (x y : M), r x y → ↑s x y} ≤ c",
"state_before": "M : Type u_1\nN : Type ?u.26925\nP : Type ?u.26... | [
529,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
528,
1
] |
Mathlib/Topology/Connected.lean | isOpen_connectedComponent | [
{
"state_after": "α : Type u\nβ : Type v\nι : Type ?u.114625\nπ : ι → Type ?u.114630\ninst✝¹ : TopologicalSpace α\ns t u v : Set α\ninst✝ : LocallyConnectedSpace α\nx : α\n⊢ IsOpen (connectedComponentIn univ x)",
"state_before": "α : Type u\nβ : Type v\nι : Type ?u.114625\nπ : ι → Type ?u.114630\ninst✝¹ : T... | [
1160,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1157,
1
] |
Mathlib/Logic/Equiv/TransferInstance.lean | Equiv.nontrivial | [] | [
433,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
11
] |
Mathlib/Algebra/CharZero/Lemmas.lean | nat_mul_inj' | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝² : NonAssocRing R\ninst✝¹ : NoZeroDivisors R\ninst✝ : CharZero R\nn : ℕ\na b : R\nh : ↑n * a = ↑n * b\nw : n ≠ 0\n⊢ a = b",
"tactic": "simpa [w] using nat_mul_inj h"
}
] | [
118,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | gcd_eq_normalize | [] | [
371,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
] |
Mathlib/Analysis/Calculus/DiffContOnCl.lean | DiffContOnCl.differentiable_at' | [] | [
86,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/CategoryTheory/PathCategory.lean | CategoryTheory.composePath_comp' | [] | [
194,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.submatrix_map | [] | [
2440,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2438,
1
] |
Mathlib/CategoryTheory/Idempotents/Karoubi.lean | CategoryTheory.Idempotents.Karoubi.p_comm | [
{
"state_after": "no goals",
"state_before": "C : Type u_1\ninst✝ : Category C\nP Q : Karoubi C\nf : Hom P Q\n⊢ P.p ≫ f.f = f.f ≫ Q.p",
"tactic": "rw [p_comp, comp_p]"
}
] | [
97,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Init/Logic.lean | AsTrue.get | [] | [
431,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
429,
1
] |
Mathlib/Data/Int/Log.lean | Int.log_zpow | [
{
"state_after": "case intro.inl\nR : Type u_1\ninst✝¹ : LinearOrderedSemifield R\ninst✝ : FloorSemiring R\nb : ℕ\nhb : 1 < b\nn : ℕ\n⊢ log b (↑b ^ ↑n) = ↑n\n\ncase intro.inr\nR : Type u_1\ninst✝¹ : LinearOrderedSemifield R\ninst✝ : FloorSemiring R\nb : ℕ\nhb : 1 < b\nn : ℕ\n⊢ log b (↑b ^ (-↑n)) = -↑n",
"st... | [
142,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/LinearAlgebra/Basis/Bilinear.lean | LinearMap.sum_repr_mul_repr_mul | [
{
"state_after": "ι₁ : Type u_5\nι₂ : Type u_6\nR : Type u_1\nR₂ : Type ?u.52670\nS : Type ?u.52673\nS₂ : Type ?u.52676\nM : Type ?u.52679\nN : Type ?u.52682\nP : Type ?u.52685\nMₗ : Type u_2\nNₗ : Type u_4\nPₗ : Type u_3\ninst✝¹⁷ : CommSemiring R\ninst✝¹⁶ : CommSemiring S\ninst✝¹⁵ : CommSemiring R₂\ninst✝¹⁴ : ... | [
70,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/GroupTheory/Perm/Fin.lean | Fin.coe_cycleRange_of_le | [
{
"state_after": "n : ℕ\ni j : Fin (Nat.succ n)\nh : j ≤ i\n⊢ ↑(if j = i then 0 else j + 1) = if j = i then 0 else ↑j + 1",
"state_before": "n : ℕ\ni j : Fin (Nat.succ n)\nh : j ≤ i\n⊢ ↑(↑(cycleRange i) j) = if j = i then 0 else ↑j + 1",
"tactic": "rw [cycleRange_of_le h]"
},
{
"state_after": "c... | [
199,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
] |
Mathlib/LinearAlgebra/Projection.lean | Submodule.coe_prodEquivOfIsCompl | [] | [
113,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Data/Real/Pi/Bounds.lean | Real.pi_gt_314 | [
{
"state_after": "no goals",
"state_before": "⊢ 3.14 < π",
"tactic": "pi_lower_bound [99 / 70, 874 / 473, 1940 / 989, 1447 / 727]"
}
] | [
174,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/Order/Minimal.lean | Set.Subsingleton.maximals_eq | [
{
"state_after": "case inl\nα : Type u_1\nr r₁ r₂ : α → α → Prop\nt : Set α\na b : α\nh : Set.Subsingleton ∅\n⊢ maximals r ∅ = ∅\n\ncase inr.intro\nα : Type u_1\nr r₁ r₂ : α → α → Prop\nt : Set α\na b x : α\nh : Set.Subsingleton {x}\n⊢ maximals r {x} = {x}",
"state_before": "α : Type u_1\nr r₁ r₂ : α → α → ... | [
126,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.I_mul_I | [] | [
334,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.lt_min'_iff | [] | [
1378,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1377,
1
] |
Mathlib/RingTheory/Coprime/Basic.lean | IsCoprime.neg_left | [
{
"state_after": "case intro.intro\nR : Type u\ninst✝ : CommRing R\nx y a b : R\nh : a * x + b * y = 1\n⊢ IsCoprime (-x) y",
"state_before": "R : Type u\ninst✝ : CommRing R\nx y : R\nh : IsCoprime x y\n⊢ IsCoprime (-x) y",
"tactic": "obtain ⟨a, b, h⟩ := h"
},
{
"state_after": "case intro.intro\n... | [
358,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
1
] |
Mathlib/Topology/Homotopy/Basic.lean | ContinuousMap.Homotopy.continuous | [] | [
139,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
11
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.sub_imJ | [] | [
933,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
933,
9
] |
Mathlib/Topology/Semicontinuous.lean | IsOpen.upperSemicontinuousAt_indicator | [] | [
750,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
748,
1
] |
Mathlib/GroupTheory/GroupAction/ConjAct.lean | ConjAct.smul_def | [] | [
150,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.Perm.eq_of_prodExtendRight_ne | [
{
"state_after": "α₁ : Type u_2\nβ₁ : Type u_1\ninst✝ : DecidableEq α₁\na✝ : α₁\ne✝ e : Perm β₁\na a' : α₁\nb : β₁\nh : a' ≠ a\n⊢ ↑(prodExtendRight a e) (a', b) = (a', b)",
"state_before": "α₁ : Type u_2\nβ₁ : Type u_1\ninst✝ : DecidableEq α₁\na✝ : α₁\ne✝ e : Perm β₁\na a' : α₁\nb : β₁\nh : ↑(prodExtendRigh... | [
842,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
839,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.transfer_eq_map_of_le | [
{
"state_after": "no goals",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu v : V\np : Walk G u v\nH : SimpleGraph V\nhp : ∀ (e : Sym2 V), e ∈ edges p → e ∈ edgeSet H\nGH : G ≤ H\n⊢ Walk.transfer p H hp = Walk.map (Hom.mapSpanningSubg... | [
1693,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1691,
1
] |
Mathlib/GroupTheory/QuotientGroup.lean | QuotientGroup.congr_refl | [
{
"state_after": "case h.mk\nG : Type u\ninst✝³ : Group G\nN : Subgroup G\nnN : Subgroup.Normal N\nH : Type v\ninst✝² : Group H\nG' : Subgroup G\nH' : Subgroup H\ninst✝¹ : Subgroup.Normal G'\ninst✝ : Subgroup.Normal H'\nhe : optParam (Subgroup.map (↑(MulEquiv.refl G)) G' = G') (_ : Subgroup.map (MonoidHom.id G)... | [
330,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
1
] |
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